多点边值问题的插值矩阵法及误差分析

插值矩阵法是求解多点边值问题的数值法。本文给出的该法的误差分析,论证了插值矩阵法解得的y(x),y'(x),…,y^(m)(x)有相同的精度,并对二阶方程,给出该法的稳定性证明和收敛阶。     

相关变量随机数序列产生方法

当采用蒙特卡罗方法对很多问题进行研究时,有时需要对多维相关随机变量进行抽样.之前的研究表明:在协方差矩阵满足正定条件时,可以采用Cholesky分解方法产生多维相关随机变量.本文首先对产生多维相关随机变量的理论公式进行了推导,发现采用Cholesky分解并不是产生多维相关随机变量的唯一方法,其他的矩阵分解方法只要能满足协方差矩阵的分解条件,同样可以用来产生多维相关随机变量.同时给出了采用协方差矩阵、相对协方差矩阵和相关系数矩阵产生多维随机变量的公式,以方便以后使用.在此基础上,利用一个简单测试题和Jacobi矩阵分解方法对上述理论进行了验证.通过对大亚湾中微子能谱进行抽样分析,Jacobi矩阵分解和Cholesky矩阵分解结果一致.针对核工程中的不确定性分析常用的~(238)U辐射俘获截面协方差矩阵进行分解时,由于协方差矩阵的矩阵本征值有负值,导致很多矩阵分解方法无法使用,在引入置零修正以后发现,与Cholesky对角线置零修正相比,Jacobi负本征值置零修正的误差更小.     

基于光纤光栅的应变与温度分离技术的研究

理论分析了光纤光栅交叉敏感的物理机制,重点研究了基于双波长矩阵法和双参量矩阵法的应变与温度分离技术。提出了一种基于双参量矩阵法的应变与温度测量系统,该系统传感头由FBG和非本征型F-P干涉腔(EF-PI)构成,其中FBG对应变敏感,EFPI测温精度高。     

矩阵角条件数与病态方程组

本文在「１」的基础上量化矩阵角条件数，分析矩阵各种条件数的联系与区别，分析系统矩阵条件数对线性代数方程组 妥的影响，进一步批明加速后的行处理法是求解严重病态线性代数方程组的可取方法。     

光纤光栅法布里-珀罗腔的V-I传输矩阵法研究

快速有效地获得多级联光纤光栅法布里-珀罗(F-P)腔的光谱特性,是优化设计基于上述结构建立的级联多波长激光器、放大器等各种光器件以及复杂分布式传感网络的重要基础和保障.将V-I传输矩阵法用于光纤光栅F-P腔反射光谱特性的分析,并建立了V-I传输矩阵模型.采用该模型对三种不同结构的光纤光栅F-P腔在不同参数下的光谱特性进行分析,并与传统多层膜法的分析结果相比较,表明V-I传输矩阵法能够在保证分析精度的前提下大大节省运算时间.实验结果表明,V-I传输矩阵法对光纤光栅F-P腔谱特性的分析结果比耦合模法更准确.     

局部横向压力条件下光纤光栅偏振相关损耗谱次峰研究

研究了局部压力条件下光纤光栅偏振相关损耗(PDL)的光谱表征。针对次峰现象,详细研究了压力幅度、受压长度和受压位置对次峰产生条件的影响。采用传输矩阵法进行了数值模拟,理论分析和数值仿真显示,受压长度对次峰随压力变化的幅度和波长位移灵敏度有重要影响。在不同的受力长度下,产生次峰需要的受力幅度不同。该研究对利用PDL次峰进行传感具有很好的理论指导意义。     

局部横向压力条件下光纤光栅偏振相关损耗谱次峰研究EI北大核心CSCD

研究了局部压力条件下光纤光栅偏振相关损耗(PDL)的光谱表征。针对次峰现象,详细研究了压力幅度、受压长度和受压位置对次峰产生条件的影响。采用传输矩阵法进行了数值模拟,理论分析和数值仿真显示,受压长度对次峰随压力变化的幅度和波长位移灵敏度有重要影响。在不同的受力长度下,产生次峰需要的受力幅度不同。该研究对利用PDL次峰进行传感具有很好的理论指导意义。     

HXMT探测器能量响应矩阵的计算

介绍硬X射线调制望远镜(HXMT)探测器能量响应矩阵的计算方法，根据实验室测量数据计算了该条件下的能量响应矩阵；利用该能量响应矩阵由直接解调法解实验室所测放射源能谱，能很好地重现放射源能量.     

基于奇异值分解的数字波前拟合算法

提出了基于奇异值分解、采用泽尼克多项式拟合干涉波前的算法,该算法直接从线性方程组入手,对矩阵进行奇异值分解分解,在求解逆矩阵的过程中,采用阈值法对奇异值的倒数进行非常规的置换(∞→0),可直接得到系数向量。理论分析和实验证明,相对于传统的格拉姆施密特正交法,该算法可首先通过求解条件数判断线性方程矩阵是否奇异,对于解决病态方程组或奇异矩阵的最小二乘问题,有很好的稳定性,避免了由最小二乘构造的法方程组出现病态而引入的计算误差,且易于编程。     

斯托克斯矢量法在全光纤电流传感器中的应用

针对目前全光纤电流传感器中光信号检测环节多是采用双路光强分析偏振度这一现状,提出将斯托克斯矢量法应用于光纤电流传感器信号偏振度的演变分析,在近似条件下,推导得到基于穆勒矩阵的光纤电流传感器简化传输矩阵.从琼斯矢量法和实验结果的比较可知,斯托克斯矢量法与琼斯矢量法的模拟效果十分接近,此外它还具有传输矩阵中不存在复数、容易简化为稀疏矩阵以及最终偏振度只需计算总传输矩阵的第2个对角元即可等运算优势.这些优势使得该方法不仅可以很好地进行理论分析,还可以有效地简化分析过程和运算过程.     

解线性代数方程组的TCG迭代法

ICCG方法是解线性代数方程组较为理想的方法,但它仅适用于具有正定对称的系数阵。本文介绍的TCG方法便足改造过的ICCG方法,它适用于一般非奇异的非正定对称阵。TCG方法比常用的JLUCG方法,对于非定常问题,可提高效率18%,特别是取用SIP不完全L、U分解作预条件时,可提高效率40%,是计算非正定对称阵较为理想的迭代法之一。本文推导出在消去法不完全L,U分解下的TCG方法,并用数值结果论证出它比ILUCG方法加速收敛的所在。     

论具有恒定通量的复杂非线性网络的试探解法

本文将网络变换法推广于解任意复杂的具有恒定通量的非线性网络,在应用这种方法时,从网络几何的观点上研究了寻求最佳解案的问题,并获得了一些初步结果。在附录1中将王显荣建议的解法——克希荷夫方程法和本文介绍的网络变换法作了一些比较。在附录2中,研究了其中包含有可分出来的线性网络部份的非线性网络,得到了当这种网络包含有任意多个非线性元件时的解案。     

A single external cavity laser-based sensor for simultaneous detection and quantification of atmospheric methane and water vapor

A single external cavity diode laser (ECDL)-based sensor system was developed for simultaneous measurements of methane and water vapor in the atmospheric air. A home-made continuous wave (CW) ECDL with a wavelength of \(\sim\) 1325 nm was employed to cover two absorption lines for different gas species. A high-finesse optical cavity composed of two high-reflectivity mirrors (\(R=0.99927\)) was used to enhance the gas absorption in a space of 0.5 l. An isolated methane absorption line at \(7552.74 \hbox { cm}^{-1}\) and a common (non-isolated) absorption line of water vapor and methane \(7552.81\hbox {cm}^{-1}\) were utilized for simultaneous detection. A method was developed to calculate the water vapor concentration from these lines. To our knowledge, the method and the absorption lines used in the present paper were used for the first time for simultaneous measurement of the concentrations of atmospheric methane and water vapor.     

Dispersion and lifetimes of electromagnetic modes attached to strongly textured slab waveguides

The influence of strong, two-dimensional (2D) periodic texture on the dispersion and lifetimes of resonant electromagnetic modes localized in the vicinity of thin (80 to 155 nm) GaAs membranes supported on thick (1 to 2 m) wet-oxidized AlAs cladding layers is reported. A method of extracting this information by fitting Fano-like features in broadband specular reflectivity spectra is described in detail, and applied to samples containing both triangular and square 2D lattices. A new and easier method of probing the properties of these modes is also demonstrated. It involves incorporating a superlattice of defects in the principal crystal lattice, and monitoring the defect diffraction spectrum, rather than the specular reflectivity.     

Solid-Phase Luminescence Determination of Ciprofloxacin and Norfloxacin in Biological Fluids

A simple, rapid, and sensitive luminescence test method for the determination of ciprofloxacin (CIP) and norfloxacin (NOR) has been described. The method is based on the intramolecular energy transfer from organic acid to terbium (Tb³⁺) ion. Luminescence of terbium (III) complex with CIP (NOR), sorbed on the zeolite has been studied. Under optimized conditions the detection limit is 1 g/mL in urine and human plasma.     

用Ge(Li)探测器测量正电子3γ湮没

本文提出了用Ge(Li)探测器测量正电子3γ湮没的方法,只测量511keV峰区计数,就能确定3γ湮没与2γ湮没的相对份额。我们称这种方法为“峰法”。对“峰法”和“峰-谷法”的结果进行了比较。 关键词：     

The OPCL control method for entrainment,model-resonance,and migration actions on multiple-attractor systems

A survey is given of three different control objectives that can be achieved with the use of the Open-Plus-Closed-Loop (OPCL) control method, developed by Jackson and Grosu. For a system that can be characterized by N first-order ordinary differential equations, these objectives are: (1) the asymptotic entrainment of the system's dynamics to a prescribed "goal" dynamics, g(t); (2) an experimental-search method to determine an approximate dynamic model; (3) the transferal of the system from one attractor to any "target" attractor. For one class of systems, this may be accomplished without a model, by using only a short-duration record of the natural dynamics in the target attractor, as demonstrated experimentally using the Chua system. (c) 1997 American Institute of Physics.     

Three-electron auger process from beam-foil excited multiply charged ions

Electron emission from collisions of C3+ ions (22.7 A MeV) with carbon foils (21, 49 and 90 microg/cm(2)) was studied by the time-of-flight method. Two prominent emission patterns can be readily identified as "binary encounter" electrons and "cusp" electrons. With the thinnest target only, a third structure is visible at slightly lower time-of-flight (thus slightly higher energy) than the cusp electrons. The energy of these electrons would correspond to 647(+116)/(-104) eV if they were emitted from the projectile frame of reference. A possible explanation is a rare three-electron-Auger K(2)L(2)L(1) process.     

An Improvement of Spatial Carrier Phase-shifting Method

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An Improvement of Spatial Carrier Phase-shifting Method

Spatial-carrier phase-shifting method (SCPM) retrieves the phase distribution from carrier interferograms by assuming that the phases of the processed pixel and its adjacent pixels are uniform,which introduces considerable theoretical error. A new method is presented in this paper to improve the SCPM accuracy: (1) A quadric curve is used to describe the phase distribution of the adjacent pixels; (2) The linear and quadric terms of the phase are considered as phase shifter errors; (3)Suitable phase shifting algorithms insensitive to these errors are selected. Two "5-step" algorithms are used and their properties are analyzed. An example ofphase retrieving by SCPM is given and the result shows that SCPM has high theoretical accuracy. With the potential high accuracy, ability of measuring dynamic phase andcomputational simplicity, SCPM will become a much more useful phase measurement method.